Elimination graph
= Elimination graph
One step of symmetric <Gaussian elimination> removes the pivot vertex and connects its remaining neighbors into a <clique>. The rule follows from the <Schur complement> update $a_{ij}\leftarrow a_{ij}-a_{ik}a_{kj}/a_{kk}$. Repeating it predicts the generic factor sparsity; exceptional numerical cancellations can remove structurally predicted entries.